|as to account for the motion of various objects.|
|3. ||They then checked these qualitative statements to assess whether any intractable difficulties were likely to arise in applying the method.|
|4. ||Only then did these skilled problem solvers begin to apply the method quantitatively to produce mathematical equations.|
In all cases, once a problem solver had selected a method and begun writing
any equations, he was then successful in applying that selected method to solve
the problem.Thus in several diverse settings it seems that low-detail, qualitative, often
vague reasoning is crucial to effective problem solving, particularly at the beginning of the problem-solving process. What are the implications for science
instruction?Students often think that qualitative reasoning (e.g., with diagrams or
sketches) is illegitimate in the context of science. The reasons for this bias are
clear. For want of space and time, textbook authors and lecturers commonly
present only the final precise, mathematical form of an argument. They omit
the initial stages in which qualitative low-detail reasoning is used to plan more
detailed work. Thus students infer that all reasoning in science should be
quantitative, and they are often puzzled about how such reasoning is done. For
example, students often say things like, "I can follow all your reasoning, but I
can't see how you decided what to do."The examples of research I've mentioned here suggest that the qualitative
reasoning so often omitted is crucial to the process of "deciding what to do."
What is needed is instruction aiding in using qualitative reasoning effectively to
plan more detailed work.
I've talked about three ideas which seem to be central to information processing models in several areas. These ideas are:
|1. ||The importance of specifying not just actions, but also the conditions under
which those actions can usefully be executed.|
|2. ||The importance of large-scale functional units--"scripts" or "methods"
which a problem solver can use in place of piecemeal assemblying individual
items of information.|
|3. ||The importance of low-detail qualitative reasoning to plan problem solutions
before execution of details.|
All three of these ideas could, I think contribute substantively to good science
instruction, which too often focuses on what to do (and not on when to do it); on
individual principles (rather than coherent methods); and on precise
mathematical techniques (rather than more global qualitative reasoning).